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woops, i read the first two sentences and i thought it was a classic question we had in our math book so i just typed it but then i read the whole thing and it turned out it wasn't like that  sorry
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I got the last question I tried to help wrong so take this with a grain of salt 
Using a^2 + b^2 = c^2, let:
a = distance from flag pole to car
b = height of flagpole
c = hypotenuse
Differentiating both sides with respect to t: 2a(da/dt) + 2b(db/dt) = 2c(dc/dt)
db/dt is the rate of change of the height of the flagpole, which is 0, so you get rid of 2b(db/dt), while da/dt is the rate of change of the distance from flag pole to car, which is 3ft/sec, so:
2a x 3 = 2c(dc/dt)
dc/dt = 3a/c
When the flag is 20 ft from the ground, which means 20ft of rope is to the right of the pole in the diagram, the hypotenuse is 120-20ft = 100ft (so c=100)
Using pythagoras the distance from the pole to car at that time must be sqrt(100^2-40^2) (so a=sqrt(100^2-40^2))
Substituting into dc/dt = 3a/c gives 3x(sqrt(100^2-40^2))/100 = 2.75ft/sec
dc/dt is the rate at which the length of the hypotenuse is changing, so this must be equal to the rate at which the flag is rising because their lengths add to a total of 120ft, so I think 2.75ft/sec is the answer.
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lol, this is just a play that makes you solve for dc/dt. Height is a constant and doesn't change (it is the flag pole, not the flag), so simply use what you have already given a constant (db/dt = 0), 2a da/dt = 2c dc/dt, c = 120-(40-20), solve for a yourself, plug in.
EDIT - Skyglow got to it first with an identical and better explained solution, I can't be too wrong I guess :p
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Thanks a bunch, I understand in fully now. ^^
The second one was really easy though, so no worries haha. The first one confused me a bit, but thanks a lot skyglow1 and Ecael ^^.
This can be closed now!
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Ok guys, I need help again.......
I need to find the critical points and then the interval on which the function is increasing and decreasing. We need to apply the First Derivative Test.
The question: y=x(x+1)^3
I know I need to find the derivative of y, but I don't know what to do after that, the teacher didn't go over this and this hw assignment is due in recitation tomorrow morning.......=/
And the second one is: Find the minimum value of f(x)=x^x for x>0. I got 0.37. Is that the correct answer?
And finally:
A particle moves counterclockwise around the ellipse 9x^2 + 16y^2 = 25.?
a) In which of the four quadrants is the derivative dx/dt positive? Explain.
b) Find a relation between dx/dt and dy/dt.
c) At what rate is the x-coordinate changing when the particle passes the point (1,1) if its y-coordinate is increasing at a rate of 6ft/s?
Sorry, I somewhat get it, but not really >_<
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At critical values the function has a horizontal slope. Before those points the function either ascends or descends and will do so at an increasingly slower rate. Until them the slope becomes zero and hence the line of tangency will be parallel with the x-axis. Then it can either ascend or descend again. If it does the opposite of what it did first that critical point will be a maximum or minimum valley. A 'peak' or 'valley' so to speak. If it goes on doing the same thing it's still a critical point. It's just that it doesn't change direction.
If the slope is zero then f'(x) is zero. So get the first derivative and solve for zero. Then you need to check what happens before and after that point to know what kind of critical point it is.
http://en.wikipedia.org/wiki/First_derivative_test
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kkkkkkkk 
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EPT
